On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State
@article{Wei2018OnTE,
title={On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State},
author={Lu Wei},
journal={Entropy},
year={2018},
volume={21}
}The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of the Tsallis entropy that involves finite sums of some terminating hypergeometric functions. In the special cases of quadratic entropy and small subsystem dimensions, the main result is further simplified to…
14 Citations
Skewness of von Neumann entanglement entropy
- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020
In proving the main result, this work obtains as a byproduct various summation identities involving polygamma and related functions that leads to an improved approximation to the distribution of von Neumann entropy.
Entropy fluctuation formulas of fermionic Gaussian states
- Computer ScienceArXiv
- 2022
The main results of this work are the exact yet explicit formulas of variances for both cases of particle number constrain, and the key ingredient in proving the results relies on a new simplification framework.
Exact variance of von Neumann entanglement entropy over the Bures-Hall measure
- Computer SciencePhysical review. E
- 2020
This work studies the statistical behavior of quantum entanglement over the Bures-Hall ensemble as measured by von Neumann entropy, and obtains a simple but accurate Gaussian approximation of the distribution of vonNeumann entropy of finite-size systems.
Average capacity of quantum entanglement
- Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2023
The exact and asymptotic formulas of average capacity have been derived under the Hilbert–Schmidt and Bures-Hall ensembles under the underlying orthogonal polynomials and special functions.
Second-order statistics of fermionic Gaussian states
- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2022
The main results are the exact yet explicit formulas of the two considered second-order statistics for fixed subsystem dimension differences and the exact variance of von Neumann entropy valid for arbitrary subsystem dimensions.
Bures–Hall ensemble: spectral densities and average entropies
- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019
We consider an ensemble of random density matrices distributed according to the Bures measure. The corresponding joint probability density of eigenvalues is described by the fixed trace Bures–Hall…
Quantum interpolating ensemble: Average entropies and orthogonal polynomials
- Computer ScienceArXiv
- 2021
A generalized ensemble of density matrices, termed quantum interpolating ensemble, which is able to interpolate between these two seemingly unrelated ensembles, and derives the exact mean formulas of entanglement entropies over such an ensemble generalizing several recent results in the literature.
From Rényi Entropy Power to Information Scan of Quantum States
- Computer ScienceEntropy
- 2021
This paper proposes generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality, and provides a convenient technical framework for the derivation of a one-parameter family of Rényi-entropy-power-based quantum-mechanical uncertainty relations.
Generalized Entropies, Variance and Applications
- Mathematics, Computer ScienceEntropy
- 2020
The dynamic version of the mentioned notions is studied through the residual lifetimes and suitable aging notions, and some findings of interest in reliability theory are achieved, such as a characterization for the exponential distribution, various results on k-out-of-n systems, and a connection to the excess wealth order.
Generation of Bures-Hall mixed states using coupled kicked tops
- Physics
- 2021
We simulate a system of coupled kicked tops to generate random density matrices distributed according to the Bures-Hall measure, which has an important role in quantum information theory. We study…
References
SHOWING 1-10 OF 19 REFERENCES
Average entropy of a subsystem from its average Tsallis entropy.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002
In the non-extensive Tsallis scenario, Page's conjecture for the average entropy of a subsystem [Phys. Rev. Lett. 71, 1291 (1993)] as well as its demonstration are generalized, i.e., when a pure…
Bures–Hall ensemble: spectral densities and average entropies
- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019
We consider an ensemble of random density matrices distributed according to the Bures measure. The corresponding joint probability density of eigenvalues is described by the fixed trace Bures–Hall…
Random pure states: Quantifying bipartite entanglement beyond the linear statistics.
- MathematicsPhysical review. E
- 2016
The properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions N and M are analyzed, and a general relation between the n-point densities and the cross moments of the eigenvalues of the reduced density matrix is established.
Typical entropy of a subsystem: Page curve and its variance.
- Physics, Computer Science
- 2019
For a system of non-interacting spins in a magnetic field, the thermal entropy arises as the typical entanglement entropy of a subsystem as well as the application to physical systems in an energy eigenstate.
Information Invariance and Quantum Probabilities
- Mathematics
- 2009
We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually…
A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy
- MathematicsPhysical review. E
- 2017
A proof of the conjecture that for a quantum system of Hilbert dimension mn in a pure state, the variance of the von Neumann entropy of a subsystem of dimension m≤n is given by ψ_{1}(·) is the trigamma function is given.
Possible generalization of Boltzmann-Gibbs statistics
- Physics
- 1988
With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelySq ≡k [1 – ∑i=1W piq]/(q-1), whereq∈ℝ characterizes the generalization andpi are the…
Proof of Page's conjecture on the average entropy of a subsystem.
- MathematicsPhysical review letters
- 1994
A proof of this elegant formula is outlined that if a quantum system of Hilbert space dimension [ital mn] is in a random pure state, the average entropy of a subsystem of dimension[ital m][le][ital n] is given by [ital S], which is equivalent to 1/[ital k][minus]1/2[ital n].
Average Entropy of a Quantum Subsystem.
- MathematicsPhysical review letters
- 1996
It was recently conjectured by D. Page that if a quantum system of Hilbert space dimension {ital nm} is in a random pure state then the average entropy of a subsystem of dimension {ital m} where…